Stable optimizationless recovery from phaseless linear measurements

Paul Hand

MIT

We will discuss the problem of recovering an n-vector from m linear
measurements lacking sign or phase information. We will use the
technique of lifting to pose a semidefinite relaxation of the problem.
In this setting, the n-vector can be recovered with high probability
if m = O(n log n). The recovery method is optimizationless in the
sense that trace minimization is unnecessary. We further demonstrate
that the algorithm of projection onto convex sets converges linearly
toward the unique solution.